Battery Management System

ABSTRACT

A method includes receiving current measurements from at least one current sensor configured to measure current of a battery system in communication with a power distribution network having a power plant. The method also includes receiving voltage measurements from at least one voltage sensor configured to measure voltage of the battery system and temperature measurements from at least one temperature sensor configured to measure temperature of the battery system. The method includes determining an impedance parameter of the battery system based on the received measurements, a temperature parameter of the battery system based on the received measurements, a predicted voltage parameter based on the impedance parameter, and a predicted temperature parameter based on the temperature parameter. The method includes commanding the battery system to charge power from the power plant or discharge power from the power plant based on the predicted voltage parameter and the predicted temperature parameter.

CROSS REFERENCE TO RELATED APPLICATIONS

This U.S. patent application claims priority under 35 U.S.C. §119(e) toU.S. Provisional Application 62/365,455, filed on Jul. 22, 2016. Thedisclosure of this prior application is considered part of thedisclosure of this application and is hereby incorporated by referencein its entirety.

TECHNICAL FIELD

This disclosure relates to predicting a battery management systemperformance based on a time series analysis and a neural network ofhistorical data of a battery system associated with the batterymanagement system.

BACKGROUND

A battery management system (BMS) is an electronic system that manages arechargeable battery system that includes one or more cells or batterypacks. The BMS may protect the battery from operating outside a safeoperating region and monitor a state of the battery (e.g., voltage,temperature, current, etc.). In addition, the BMS may calculate dataassociated with the battery and report the calculated data to externaldevices for monitoring, controlling the environment of the batterysystem, and authenticating and/or balancing the battery system. Abattery built together with a BMS having an external communication busbecomes a smart battery.

The rechargeable battery system may be configured to store electricalenergy on a large scale within an electrical power grid. For example,electrical energy is stored during times when production (for example,from intermittent power plants, such as renewable electricity sources,such as wind power, tidal power, solar power) exceeds consumption, andis returned to the grid when production falls below consumption. Assuch, the rechargeable battery system stores electrical energy when gridconsumption is low and uses the stored electrical energy at times whenconsumption exceeds production from the power plant.

SUMMARY

One aspect of the disclosure provides a method implemented on dataprocessing hardware that includes receiving current measurements from atleast one current sensor configured to measure current of a batterysystem in communication with a power distribution network having a powerplant distributing power to one or more consumers. The method alsoincludes receiving voltage measurements from at least one voltage sensorconfigured to measure voltage of the battery system and temperaturemeasurements from at least one temperature sensor configured to measuretemperature of the battery system. The method includes determining animpedance parameter of the battery system based on the receivedmeasurements, a temperature parameter of the battery system based on thereceived measurements, a predicted voltage parameter based on theimpedance parameter, and a predicted temperature parameter based on thetemperature parameter. The method includes commanding the battery systemto charge power from the power plant or discharge power from the powerplant based on the predicted voltage parameter and the predictedtemperature parameter.

Implementations of the disclosure may include one or more of thefollowing optional features. In some implementations, determining theimpedance parameter or the temperature parameter comprises determining atransfer function H(w) of a time series f(t) defined in a time interval[−T, T], where T is an integer greater than zero. The transfer functionH(w), in a complex domain, may be defined as:

H(w)=f _(−T) ^(+T) f(t)e ^(−iωt) dt,

where w=2πF, F is a frequency of a time series of the receivedmeasurements, defined as tεR^(n) and FεC. The transfer function H(w) maybe defined as a ratio between a Fourier transform of an output variabley(t) and an input variable x(t), where the output variable y(t) is oneof the impedance parameter or the temperature parameter, and the inputvariable x(t) is one or more of the received measurements. The transferfunction H(w) in a discrete domain may be determined as:

${H(w)} = {\frac{\sum\limits_{p = 1}^{N}{{y(p)}e^{{- i}\; \omega \; p}}}{\sum\limits_{p = 1}^{N}{{x(p)}e^{{- i}\; \omega \; p}}}.}$

In some implementations, determining one of the predicted voltageparameter or the predicted temperature parameter includes executing atime series analysis implementing an auto-regressive model. Theauto-regressive model AR(p) may be defined as:

X _(t) =c+Σ _(i=1) ^(p)φ_(i) X _(t-i)+ε_(i),

where φ₁-φ_(p) are parameters of the model, c is a constant, and ε_(t)is white noise. The method may also include implementing a neuralnetwork approach, an empirical recursive method, or a Yule-Walkerapproach to determine an optimal solution of the auto-regressive modelAR(p).

In some implementations, commanding, by the data processing hardware,the battery system to charge power from the power plant includescommanding the battery system to store power from the power plant.

In some implementations, the method includes updating an impedanceprofile, a voltage profile, or a temperature profile based on thevoltage measurements or the temperature measurements.

In some implementations, determining the predicted voltage parameterincludes training the data processing hardware to generate a best fit ofthe voltage measurements or the temperature measurements. In someimplementations, predicting, by the data processing hardware, thepredicted voltage parameter or the predicted temperature parameter basedon the best fit of the voltage measurements or the temperaturemeasurements, respectively.

In some implementations, the method includes tracking, by the dataprocessing hardware, a remaining available capacity of the batterysystem. The method may also include determining, by the data processinghardware, one of a charge state or life cycle of the battery system.

Another aspect of the disclosure provides a system including dataprocessing hardware and memory hardware. The memory hardware may be incommunication with the data processing hardware and may storeinstructions that when executed on the data processing hardware causethe data processing hardware to perform operations. The operationsinclude receiving current measurements from at least one current sensorconfigured to measure current of a battery system in communication witha power distribution network having a power plant distributing power toone or more consumers. The operations also include receiving voltagemeasurements from at least one voltage sensor configured to measurevoltage of the battery system. The operations further include receivingtemperature measurements from at least one temperature sensor configuredto measure temperature of the battery system. The operations alsoinclude determining an impedance parameter of the battery system basedon the received measurements, and determining a temperature parameter ofthe battery system based on the received measurements. The operationsfurther include determining a predicted voltage parameter based on theimpedance parameter, and determining a predicted temperature parameterbased on the temperature parameter. The operations also includecommanding the battery system to charge power from the power plant ordischarge power from the power plant based on the predicted voltageparameter and the predicted temperature parameter.

Implementations of this aspect of the disclosure may include one or moreof the following optional features. In some implementations, determiningthe impedance parameter or the temperature parameter comprisesdetermining a transfer function H(w) of a time series f(t) defined in atime interval [−T,T], where T is an integer greater than zero. Thetransfer function H(w), in a complex domain, may be defined as:

H(w)=∫_(−T) ^(+T) f(t)e ^(−iωt) dt,

where w=2πF, F is a frequency of a time series of the receivedmeasurements, defined as tεR^(n) and FεE C^(n). The transfer functionH(w) may be defined as a ratio between a Fourier transform of an outputvariable y(t) and an input variable x(t), where the output variable y(t)is one of the impedance parameter or the temperature parameter, and theinput variable x(t) is one or more of the received measurements. Thetransfer function H(w) in a discrete domain may be determined as:

${H(w)} = {\frac{\sum\limits_{p = 1}^{N}{{y(p)}e^{{- i}\; \omega \; p}}}{\sum\limits_{p = 1}^{N}{{x(p)}e^{{- i}\; \omega \; p}}}.}$

In some implementations, determining one of the predicted voltageparameter or the predicted temperature parameter includes executing atime series analysis implementing an auto-regressive model. Theauto-regressive model AR(p) may be defined as:

X _(t) =c+Σ _(i=1) ^(p)φ_(i) X _(t-i)+ε_(i),

where φ_(i)-φ_(p) are parameters of the model, c is a constant, andε_(t) is white noise. The method may also include implementing a neuralnetwork approach, an empirical recursive method, or a Yule-Walkerapproach to determine an optimal solution of the auto-regressive modelAR(p).

In some implementations, commanding the battery system to charge powerfrom the power plant includes commanding the battery system to storepower from the power plant.

In some implementations, the operations include updating an impedanceprofile, a voltage profile, or a temperature profile based on thevoltage measurements or the temperature measurements.

In some implementations, determining the predicted voltage parameterincludes training the data processing hardware to generate a best fit ofthe voltage measurements or the temperature measurements. In someimplementations, the operations include predicting the predicted voltageparameter or the predicted temperature parameter based on the best fitof the voltage measurements or the temperature measurements,respectively.

In some implementations, the operations include tracking a remainingavailable capacity of the battery system and determining one of a chargestate or life cycle of the battery system.

In some implementations, determining the impedance parameter or thetemperature parameter includes determining a transfer function H(w) of atime series f(t) defined in a time interval [−T, T], where T is aninteger greater than zero. The transfer function H(w), in a complexdomain, may be defined as:

H(w)=∫_(−T) ^(+T) f(t)e ^(−iωt) dt,

where w=2πF, F is a frequency of a time series of the receivedmeasurements, defined as tεR^(n) and FεC^(n). The transfer function H(w)may be defined as a ratio between a Fourier transform of an outputvariable y(t) and an input variable x(t), where the output variable y(t)is one of the impedance parameter or the temperature parameter, and theinput variable x(t) is one or more of the received measurements. Thetransfer function H(w) in a discrete domain may be determined as:

${H(w)} = {\frac{\sum\limits_{p = 1}^{N}{{y(p)}e^{{- i}\; \omega \; p}}}{\sum\limits_{p = 1}^{N}{{x(p)}e^{{- i}\; \omega \; p}}}.}$

In some implementations, determining one of the predicted voltageparameter or the predicted temperature parameter includes executing atime series analysis implementing an auto-regressive model.

In some implementations, commanding the battery system to charge powerfrom the power plant includes commanding the battery system to storepower from the power plant.

In some implementations, the operations include updating an impedanceprofile, a voltage profile, or a temperature profile based on thevoltage measurements or the temperature measurements.

In some implementations, determining the predicted voltage parameterincludes training the data processing hardware to generate a best fit ofthe voltage measurements or the temperature measurements. Determiningthe predicted voltage parameter may also include predicting, by the dataprocessing hardware, the predicted voltage parameter or the predictedtemperature parameter based on the best fit of the voltage measurementsor the temperature measurements, respectively.

In some implementations, the instructions, when executed on the dataprocessing hardware, cause the data processing hardware to track aremaining available capacity of the battery system and determine one ofa charge state or life cycle of the battery system.

The details of one or more implementations of the disclosure are setforth in the accompanying drawings and the description below. Otheraspects, features, and advantages will be apparent from the descriptionand drawings, and from the claims.

DESCRIPTION OF DRAWINGS

FIG. 1 is a functional block diagram of an exemplary power distributionnetwork.

FIG. 2A is a functional block diagram of an exemplary controller of thepower distribution network of FIG. 1.

FIG. 2B is a schematic view of an exemplary arrangement of operationsfor a method of predicting a performance of an energy storage system.

FIG. 2C is a functional block diagram of an exemplary controller of thepower distribution network of FIG. 1.

FIG. 3 is a functional block diagram of an exemplary artificial neuralnetwork.

FIG. 4 is a graph of an exemplary input current obtained from batterysystem sensors.

FIG. 5 is a graph of an exemplary voltage predicted from training andtesting the neural network of FIG. 3.

FIG. 6A is a graph of an exemplary temperature predicted from trainingand testing the neural network of FIG. 3.

FIG. 6B is a graph of an exemplary remaining capacity predicted fromtraining and testing the neural network of FIG. 3.

FIG. 6C is a detailed view of a portion of the graph of FIG. 6B.

FIG. 7 is a graph of an exemplary input current obtained from batterysystem sensors.

FIG. 8 is a graph of an exemplary voltage predicted using a Yule-Walkerapproach.

FIG. 9 is a graph of an exemplary temperature predicted using aYule-Walker approach.

FIG. 10 is a functional block diagram of an exemplary heat exchangebetween a battery system and its immediate external environment.

FIG. 11 is a graph of an exemplary calculation of the maximum andminimum temperature associated with a charging cycle.

FIG. 12 is a graph of an exemplary prediction of the heat capacity andheat associated with a charging cycle.

FIG. 13A is a graph of an exemplary current frequency regulation profileassociated with a charging cycle.

FIG. 13B is a graph of an exemplary voltage frequency regulation profileassociated with a charging cycle.

FIG. 14 is a graph of an exemplary comparison between predicted andmeasured data associated with a charging cycle.

FIG. 15A is a graph of an exemplary power profile.

FIG. 15B is a graph of exemplary measured and predicted voltages usingpower training data of the power profile shown in FIG. 15A.

FIG. 16 is a graph of an exemplary power and its associatedstate-of-charge.

FIG. 17 is a graph of an exemplary voltage profile and a minimum cut-offvoltage.

FIG. 18 provides a schematic view of an exemplary arrangement ofoperations for a method of predicting future battery system parameters.

FIG. 19 is a schematic view of an exemplary computing device executingany systems or methods described herein.

Like reference symbols in the various drawings indicate like elements.

DETAILED DESCRIPTION

FIG. 1 illustrates an exemplary power distribution network 100configured to transmit power from a power plant 110 to an energy storagesystem 120 and to individual consumers 130. The energy storage system120 includes a battery management system (BMS) 122 in communication witha rechargeable battery system 124. The battery system 124 includes powerstorage devices (e.g., batteries) configured to capture power from thepower plant 110 and store the power for distribution at a later time.The rechargeable battery system 124 stores electrical energy on a largescale within the power distribution network 100. In some examples, forlarge battery systems 124 that include multiple batteries, the behaviorof the ensemble of batteries is the same as the average behavior of theindividual batteries.

The cost to supply electricity varies during the course of a single day.As such, the wholesale price of electricity on the power distributionnetwork 100 reflects the real-time cost for supplying electricity fromthe power plant 110. For example, electricity demand is usually highestin the afternoon and early evening (peak hours), and costs to provideelectricity are usually higher at these times. Usually, most consumers130 pay prices based on the seasonal average cost of providingelectricity. Therefore, the consumers 130 do not notice the dailyfluctuation in electricity prices. As such, it is desirable to have apower distribution network 100 that is configured to store electricityduring off-peak hours and distribute the stored electricity during thepeak hours to reduce the demand on the power plant 110. In someexamples, the energy storage system 120 stores renewable energy, such asenergy produced by wind and solar, which are intermittent, and thereforethe rechargeable battery system 124 stores the intermittent renewableenergy to provide smooth electricity to the consumers 130. The consumers130 may include one or more of a house consumer 130 a, a factoryconsumer 130 b, a business consumer 130 c, or any other consumer thatreceives electrical power from the power distribution network 100.

The BMS 122 manages the rechargeable battery system 124 and protects thebattery from operating outside a safe operating state. In addition, theBMS 122 monitors the performance of the battery system 124, for example,by monitoring a voltage, a temperature, and a current of the batterysystem 124. Consequently, the BMS 122 may report the monitored data to acontroller 200. In some examples, the BMS 122 performs calculations onthe monitored data before sending the data to the controller 200; whilein other examples, the BMS 122 sends the controller 200 the raw data.

The energy storage system 120 may be in communication with thecontroller 200 via a network 10. The network 10 may include varioustypes of networks, such as a local area network (LAN), wide area network(WAN), and/or the Internet. The controller 200 receives data from theBMS 122, e.g., from sensors 123 associated with the battery system 124of the energy storage system 120, and monitors the sensors 123 topredict the performance of the battery system 124. As such, thecontroller 200 executes a series analysis of the received data 126 fromthe sensors 123.

Referring additionally to FIGS. 2A and 2B, the initial cycles ofreceived data 126 from the sensors 123 are considered as learning cyclesor learning parameters, which are used to predict animpedance/resistance profile (at impedance transfer function 242) thatis applied to predict the voltage (at voltage prediction 252 b) andtemperature (at temperature prediction 254 b). Since the controller 200continuously receives the data 126 from the sensors 123, for example,via the network 10, the controller 200 continuously updates the profileof the resistance and therefore the profiles of the voltage andtemperatures. As such, the controller 200 may execute algorithms topredict the performance of the battery system 124 and use the predictedmetrics to bid on the electrical power of the BMS into the market.

As will be described in more detail below, the learning cycles orlearning parameters utilized by the algorithms described herein allowthe controller 200 to predict future performance of the battery system124 to avoid failures thereof and to accurately and efficient instructthe BMS 122 to transmit energy to or from the battery system 124 forstorage or use. For example, by utilizing previously generated data 126,the algorithms allow the BMS 122 to predict the future performance ofthe battery system 124 and make decisions (e.g., instruct the batterysystem 124 to store electrical power or discharge electrical power) toincrease the efficiency and longevity of the energy storage system 120.Utilization of the learning cycles by the algorithms allows the BMS 122to learn from previously generated data 126 transmitted from the sensors123 in order to build accurate models that predict future performance ofthe battery system 124. The predictions and decisions made by the BMS122 increase the efficiency and longevity of the battery system 124relative to battery management systems relying on rigid, static rules.For example, modeling and optimization based on the previously generateddata 126 increases the accuracy of quantified measurements of the data126, while adjusting decisions and outcomes in response to changes inthe data 126 ensures accurate measurements and interpretation of thedata 126. The utilization of robust programming protocols or procedures(e.g., C++ procedures) reduces the amount of time required for thecontroller 200 to execute the algorithms described herein.

The controller 200 includes memory hardware 210 that stores instructionsand data processing hardware 220 that executes the instructions toperform one or more operations. The memory hardware 210 may be physicaldevices used to store programs (e.g., sequences of instructions) or data(e.g., program state information) on a temporary or permanent basis foruse by a computing device. The non-transitory memory may be volatileand/or non-volatile addressable semiconductor memory. Examples ofnon-volatile memory include, but are not limited to, flash memory andread-only memory (ROM)/programmable read-only memory (PROM)/erasableprogrammable read-only memory (EPROM)/electronically erasableprogrammable read-only memory (EEPROM) (e.g., typically used forfirmware, such as boot programs). Examples of volatile memory include,but are not limited to, random access memory (RAM), dynamic randomaccess memory (DRAM), static random access memory (SRAM), phase changememory (PCM) as well as disks or tapes.

The data processing hardware 220 may be in communication with the memoryhardware 210 and may execute the instructions to perform one or moreoperations. In some implementations, the data processing hardware 220executes an initial cycle extraction function 230, a transfer functioncalculation function 240, and a prediction function 250. The executedfunctions 230, 240, 250 use the captured sensor data 126 to predict thefuture performance of the energy storage system 120, specifically theBMS 122.

In some implementations, the BMS 122 includes a current sensor 123 a, avoltage sensor 123 b, and a temperature sensor 123 c associated with thebattery system 124. The data processing hardware 220 receives sensorsignals 126 a, 126 b, 126 c from each one of the current sensor 123 a,the voltage sensor 123 b, and the temperature sensor 123 c,respectively.

Training Data Selection

The initial cycle extraction function 230, the transfer functioncalculation function 240, and the prediction function 250 executed onthe data processing hardware 220 may evolve and update as more signaldata 126 is received from the BMS 122. As such, the core of thefunctions 230, 240, 250 are based on an evolving training process thatincludes the use of historical signal data 126 recorded by the BMS 122from the sensors 123 in the time interval [t, t+n] to predict the dataat cycle t+n+1, where t is a current time and n is positive numbergreater than zero.

Once the data processing hardware 220 receives the sensor data signals126, the data processing hardware 220 executes a cost function thatdefines a mathematical relationship between the different data signal126 associated with each one of the sensors 123 a, 123 b, 123 c.Accordingly, the training data is continuously evolving since theselection of the historical signal data 126 is revisited every n cycles.This continuous update of the historical signal data 126 allows thecontroller 200 to capture changes in the signal data 126 during itscycling regimen. The optimization of a training factor may depend on thecharacteristics of the BMS under-consideration.

Transfer Function

As shown in FIG. 2C, the controller 200 receives input variables, i.e.,sensor signals 126 a, 126 b, 126 c, and outputs prediction outputvariables 270 a, 270 b using training parameters 128 a, 128 b, 128 coutputted from the training data selection function 230. Morespecifically, the inputs-outputs relationship can be defined as transferfunctions (i.e., the impedance transfer function 242 and a temperaturetransfer function 244) of the controller 200.

In a continuous domain, a Fourier transform H(w) of a time series f(t)defined in the interval [−T, T], where T is an integer greater thanzero, is given by the following equation:

H(w)=∫_(−T) ^(+T) f(t)e ^(−iωt) dt  (1)

where w=2πF, F is a frequency of the time series, tεR^(n) and FεC^(n).H(w) is defined in a complex domain.

The transfer function H(w), i.e., the impedance transfer function 242and/or the temperature transfer function 244, executed by the controller200 is a ratio between the Fourier transform of the output variable y(t)and the input variable x(t) and is defined in the discrete domain as:

$\begin{matrix}{{H(w)} = {\frac{\sum\limits_{p = 1}^{N}{{y(p)}e^{{- i}\; \omega \; p}}}{\sum\limits_{p = 1}^{N}{{x(p)}e^{{- i}\; \omega \; p}}}.}} & (2)\end{matrix}$

For the voltage prediction, the transfer function is defines as

$\begin{matrix}{{H_{v}(w)} = {\frac{\sum\limits_{p = 1}^{N}{{V(p)}e^{{- i}\; \omega \; p}}}{\sum\limits_{p = 1}^{N}{{I(p)}e^{{- i}\; \omega \; p}}}.}} & \left( {2A} \right)\end{matrix}$

For the temperature prediction, the transfer function is defined as:

$\begin{matrix}{{H_{T}(w)} = {\frac{\sum\limits_{p = 1}^{N}{{T(p)}e^{{- i}\; \omega \; p}}}{\sum\limits_{i = 1}^{N}{{I(p)}e^{{- i}\; \omega \; p}}}.}} & \left( {2B} \right)\end{matrix}$

In some examples, the controller 200 uses the outputs of the transferfunction H(w) (e.g., transfer function calculation function 240) totrain a neural network 300 (FIG. 3) and to test for predictions. Thetransfer function H(w) is defined in the Fourier domain as a complexvector, having two parts: a magnitude |H| and a phase φ. Both themagnitude |H| and the phase φ of the transfer function H(w), i.e., theimpedance transfer function 242 and/or the temperature transfer function244, are used in the training and testing/prediction functions togenerate and improve the training sets used to predict the new data. Torecover the predicted voltage and temperature, the inverse Fouriertransform function may be applied to the product between the trainedtransfer function and the current Fourier transform. The magnitude ofthe current Fourier transform defines a voltage magnitude and atemperature magnitude that is obtained by converting the complex valuesinto real values for further analysis and visualization.

The magnitude |H| of the transfer function H(w) is shown by:

|H|=√{square root over (H _(real) ² +H _(imag2) ²)};  (3)

where H_(real) and H_(imag) are the real and imaginary parts of thetransfer function H(w).

The phase φ of the transfer function H(w) is shown by:

$\begin{matrix}{\varnothing = {{atan}\left( \frac{H_{real}}{H_{imag}} \right)}} & (4)\end{matrix}$

The magnitude |H| and the phase φ of the transfer function H(w) may varyover time and frequency. The magnitude |H| is used to quantify theperformance metrics and to track and monitor the voltage and temperaturedistribution over time for maintenance purposes. In some examples, thephase φ is used to show the angular differences between the measured andpredicted data. The phase φ may also be used as a metric to track phasechanges in the data that could be interpreted in some situations asdeviations from a normal stage.

The transfer function H(w) is applied to two separate transferfunctions, which are the voltage/current 270 a (impedance function 242)and the temperature/current 270 b (temperature function 244). Thetransfer function H(w) (e.g., transfer function calculation function240) outputs training parameters 128, i.e., impedance trainingparameters 128 b/128 a and temperature training parameters 128 c/128 a.

Prediction

The prediction function 250 uses current sensor data 126 a to predictthe voltage and the temperature (predicted voltage 272 a, predictedtemperature 272 b), with the previous recorded values of the voltage andthe temperature 270 a, 270 b used in the training data selection 240.The prediction function 250 includes a training step 252 and a testingstep 254. In addition, the prediction function 250 is applied to eachone of the voltage and temperature separately. The prediction function250 includes the steps of matching training impedance data 252 a,matching training temperature data 254 a, predict voltage 252 b, andpredict temperature 254 b.

Prediction: Training Step

During the training step 252 a, 254 a, the controller 200 is trained onthe historical training data 126 to generate the best fit of thetopology of the training data 126 and then uses those training entitiesto predict BMS data 272 into the future. Generally, any learning machineneeds representative examples of the data 128 in order to capture theunderlying structure that allows it to generalize to new or predictedcases. As such, the controller 200 may be considered as an adaptivefiltering, since it depends only on the intrinsic structure of the data128. In some implementations, the training step 252 a, 254 a includescross-validating the predicted BMS data 272 relative to the historicaltraining data 126 to minimize convergence errors.

As will be explained in more detail below, in some implementations, thetraining step 252 a, 254 a is optimized by combining, with thecontroller 200, for example, the inputs (e.g., current signal 126 a,voltage signal 126 b, or temperature signal 126 c) from each of thesensors (e.g., the current sensor 123 a, the voltage sensor 123 b, orthe temperature sensor 123 c, respectively) in order to reduce thequantity of learning cycles. For example, the training step 252 a, 254 amay use only the first five learning cycles as inputs to converge into aminimal convergence error.

Table (1) shows a mean square error (MSE) between the measured data(e.g., current signal 126 a, voltage signal 126 b, or temperature signal126 c) and the predicted data (e.g., predicted BMS data 272), where theerror is minimized during the training step.

TABLE 1 Predicted Predicted Predicted Predicted Predicted MSE Cycle 1Cycle 2 Cycle3 Cycle4 Cycle5 Measured 0.1460 0.0822 0.0717 0.0668 0.0224An accurate prediction of the remaining discharge time of the batterysystem 124 allows for tracking the health of the battery system 124relative to a number of charge-discharge cycles of the battery system124.

Prediction: Testing Step

During the testing step 252 b, 254 b, the controller 200 predicts newdata 272 using the overall structure captured during the training step252 a, 254 a, i.e., the best fit of the topology of the training data126. The testing step 252 b, 254 b is similar to the training step 252a, 254 a. However, in the testing step 252 b, 254 b, the current sensordata 126 a is used as the input.

Prediction: Voltage Prediction

The voltage prediction function 252 includes the training step 252 a andthe testing step 252 b. The controller 200 applies the voltageprediction function 252 to both the voltage data 126 b and thetemperature data 126 c. The current signal 126 a is considered as aknown variable of the voltage prediction function 252. In some examples,the current signal 126 a may be determined from a power of the batterysystem 124 using Ohm's law. Ohm's law states that a current through aconductor between two points is directly proportional to the voltageacross the two points, i.e., I=V/R, where I is the current through theconductor in units of voltage measured across the conductor in units ofvolts, and R is the resistance of the conductor in units of ohms.However, the controller 200 determines the resistance/impedance prior tothe application of Ohm's law.

Prediction: Temperature Prediction

The temperature prediction function 254 includes the training step 254 aand the testing step 254 b. Heat (or temperature) is an importantparameter that affects the health of the battery system 124 of theenergy storage system 120. Therefore, it is important to track thetemperature of the battery system 124 over time.

Prediction: Calculations

The controller 200 determines the prediction function 250 by using timeseries analysis. A time series is a sequence of data points drawn fromsuccessively equally spaced points in time, i.e., sensor data 126, 126b, 126 c from the sensors 123. Therefore, the time series is a sequenceof discrete-time data. Time series analysis includes a method foranalyzing the time series data to extract meaningful statistics andother characteristics of the time series data. To predict the parametersof interest, i.e., voltage and temperature, the controller 200 employsan auto-regressive (AR) model on the time series. An AR model is arepresentation of a type of random process, as such, it describescertain time-varying processes in nature, economics, etc. The AR modelspecifies that the output variable depends linearly on its own previousvalues and on stochastic term (an imperfectly predictable term). Thus,the model is in the form of a stochastic difference equation.

The notation AR(p) indicates an autoregressive model of order p. TheAR(p) model is defined as:

X _(t) =c+Σ _(i=1) ^(p)φ_(i) X _(t-i)+ε_(i);  (5)

where φ₁-φ_(p) are the parameters of the prediction function 250, c is aconstant, and ε_(t) is white noise.

Once the training parameters 128 are outputted, the training parameters128 are used to predict new data. In some examples, the controller 200determines an optimal solution of the AR model time series predictionsby executing one of a neural network approach, an empirical recursivemethod, or a Yule-Walker Approach.

Neural Network Approach

Artificial neural networks (ANNs) are a family of models inspired bybiological neural networks, such as the central nervous system ofanimals, and, in particular, the brain. The ANNs are used to estimate orapproximate functions that can depend on a large number of inputs andare generally unknown. In some examples, the ANNs are defined usingthree components: architecture rule; activity rule; and learning rule.The architecture rule of the ANNs specifies variables that are involvedin the network and their topological relationships. The activity ruledefines how the activities of neurons change in response to each other.The learning rule specifies the way in which the neural network's rightschange with time (see FIG. 3).

Referring to FIG. 3, in some implementations, a neural network 300 canbe viewed as a nonlinear system with a basic form:

F(x,w)=y;  (6)

where x is the input vector presented to the network, w is the weightvector of the network, and y is the corresponding output vectorapproximated or predicted by the network. The weight vector w iscommonly ordered first by layer, then by neurons, and finally by theweights of each neuron plus its bias.

In some examples, the controller 200 uses the Levenberg-Marquardtalgorithm to solve the nonlinear system of the neural network 300. TheLevenberg-Marquardt algorithm (LMA) is also known as the dampedleast-squares (DLS) method, and is used to solve non-linear least squareproblems. The Levenberg-Marquardt algorithm is:

(J ^(T) J+γ1)δ=J ^(T) E  (7)

where J is the Jacobian matrix for the system, γ is the Levenberg'sdamping factor, δ is the weight update vector that the controller 200 isdetermining, and E is the error vector containing the output errors foreach input vector on training network.

$\begin{matrix}{J = \begin{bmatrix}\frac{\partial{F\left( {x_{1},w} \right)}}{\partial w_{1}} & \ldots & \frac{\partial{F\left( {x_{1},w} \right)}}{\partial w_{w}} \\\vdots & \ddots & \vdots \\\frac{\partial{F\left( {x_{N},w} \right)}}{\partial w_{1}} & \ldots & \frac{\partial\left( {x_{N,}w} \right)}{\partial w_{w}}\end{bmatrix}} & (8)\end{matrix}$

where F(x_(i), w) the network function is evaluated for the i^(th) inputvector of the training set using the weight w and w_(j) is the j^(th)element of the weight vector w of the network.

For the neural network 300, the Jacobian matrix is approximated usingthe chain rule and the first derivatives of the activation functions.The chains rule is a formula for computing the derivative of thecomposition of two or more functions. For example, if f and g arefunctions, then the chain rule expresses the derivative of theircomposition.

Back propagation neural network (BPN) is a supervised learning algorithmin which the input data are supplied together with the desired output.The BPN has two hidden layers. The BPN learns during a training epoch.In this case, the BPN goes through 1000 epochs with momentum of 0.5 andlearning rate 0.5 to converge to the optimal solution in which the erroris minimized. A training epoch for each entry consists of the followingsteps: feed input data into the network; initialize weights; checkoutput against desired value and feedback error; calculate the error;and update the weights between neurons which are calculated using theLevenberg-Marquardt method. Feature selection may be applied on theinput layer of the BPN (e.g., neural network 300) using regularizationBayesian methodology to reduce redundancy and to ensure better accuracyof the output.

At each activation of the neuron of the hidden layers and the outputlayers, the weighted sums are calculated and passed through theactivation function defined as:

wSum=Σ_(i=1) ^(n)weight_(i)*input_(i).

The final adjusted weights that minimize the error are mapped into thenew input data to predict the new variables such as voltage andtemperature.

FIG. 4 shows a graph of exemplary input current data 126 a obtained froma battery system sensor 123 a. FIG. 5 shows a graph of exemplarypredicted voltage data 272 a from training and testing the neuralnetwork using the input current data 126 a obtained from the batterysystem sensors 123 a shown in FIG. 4. In addition, FIG. 6A shows a graphof exemplary predicted temperature data 272 b from training and testingthe neural network using the input current data 126 a obtained from thebattery system sensors 123 a shown in FIG. 4.

In some implementations, the controller 200 combines the inputs (e.g.,current signal 126 a, voltage signal 126 b, or temperature signal 126 c)from each of the sensors (e.g., the current sensor 123 a, the voltagesensor 123 b, or the temperature sensor 123 c, respectively) and appliesthe combined inputs as input features to train the neural network 300.FIGS. 6B and 6C show a graph of exemplary predicted remaining capacityusing the BPN. The predicted remaining capacity may correspond totraining and testing the neural network 300 using the combined inputs,as previously described. In some implementations, the predictedremaining capacity may correspond to the predicted remaining capacityduring a discharge mode of the energy storage system 120 determinedbased on a charge made of the energy storage system 120. Based on thepredicted remaining capacity measurement, the controller 200 may trackthe remaining available capacity in the energy storage system 120 (e.g.,the battery system 124) to determine a charge state or life cycle of theenergy storage system 120 (e.g., the battery system 124).

Empirical Recursive Methods

In some examples, the controller 200 predicts future measurements byusing some of the initial cycle's sensor data 126. The controllerestimates the parameters of the series based on the known AR model oforder n.

The equation that defines this operation is as follow:

$\begin{matrix}{Y_{k} = {{\alpha^{k - 1}Y_{1}} + \left( {\beta {\sum\limits_{n = 2}^{k - 1}\alpha^{k - n}}} \right) + \beta}} & (9) \\{where} & \; \\{{\alpha = \frac{\sum\limits_{i = 1}^{N}{\left( {x_{i} - \overset{\_}{x}} \right)\left( {y_{i} - \overset{\_}{y}} \right)}}{\left( \sqrt{\sum\limits_{i = 1}^{N}\left( {x_{i} - \overset{\_}{x}} \right)^{2}} \right)\left( \sqrt{\sum\limits_{i = 1}^{N}\left( {y_{i} - \overset{\_}{y}} \right)^{2}} \right)}};} & \left( {10a} \right) \\{{\beta = {\mu \left( {1 - \alpha^{2}} \right)}};} & \left( {10b} \right) \\{and} & \; \\{{\mu = {\frac{1}{N}{\sum\limits_{i = 1}^{N}x_{i}}}};} & \left( {10c} \right)\end{matrix}$

and where Y_(k) is the k^(th) time series, Y₁ is the initial cycle timeseries, α and β are respectively the slope and the intercept. Y₁ mayrepresent the initial cycles up to ten cycles and may be updated in anonline process to adjust its value.

In this method, initial cycles are considered to calculate theparameters of the algorithm. Taking into consideration Equation (9) andEquation (10), the controller 200 may predict the data into the future.The empirical auto-regressive model is evolving in computing theparameters exposed in Equation (9) and Equation (10). The initialmeasurement Y₁ (voltage or temperature) is considered to be the averageof the previous measurements. The slope and intercept are considered aswell to be the average values of the previous slope and intercept. Thismethod evolves over cycles and the parameters are updated to determinethe new values.

Yule-Walker Approach

The Yule-Walker equations provide several routes to estimating theparameters of an AR(p) model, by replacing the theoretical covarianceswith estimated values. The Yule-Walker equations include computing theautocorrelation coefficients of the previous step measurements, and thenapplying those coefficients to predict the next measurements. TheYule-Walker set of equations in solving the AR(p) model are;

$\begin{matrix}{\begin{bmatrix}\gamma_{1} \\\gamma_{2} \\\gamma_{2} \\\vdots \\\gamma_{p}\end{bmatrix} = {\begin{bmatrix}\gamma_{0} & \gamma_{- 1} & \gamma_{- 2} & \ldots & \ldots & \ldots \\\gamma_{1} & \gamma_{0} & \gamma_{- 1} & \ldots & \ldots & \ldots \\\gamma_{2} & \gamma_{1} & \gamma_{0} & \ldots & \ldots & \ldots \\\vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\\vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\\gamma_{p - 1} & \gamma_{p - 2} & \gamma_{p - 3} & \ldots & \ldots & \ldots\end{bmatrix}\begin{bmatrix}\phi_{1} \\\phi_{2} \\\phi_{2} \\\vdots \\\phi_{p}\end{bmatrix}}} & \left( {11a} \right)\end{matrix}$

This method is auto-regressive and described as:

X _(t)=Σ_(i=1) ^(p)φ_(i) X _(t-1)+ε_(i);  (11b)

where the coefficients φ_(i) are calculated based on the followingequation:

γ₀=Σ_(k=1) ^(p)φ_(k)γ_(−k)+σ_(ε) ²  (11c)

Knowing the autocorrelation γ_(k) coefficients of the previous steps,the controller 200 may determine the φ_(k) and therefore predict X_(t).In this case, the standard deviation σ_(ε) is equal to zero.

FIG. 7 shows a graph of exemplary input current sensor data 126 aobtained by the battery system sensors 123 a. FIG. 8 shows a graph ofexemplary predicted voltage data 272 a using the Yule-Walker approach;while FIG. 9 shows a graph of exemplary predicted temperature data 272 busing the Yule-Walker approach.

Quantification of the BMS Performance Metrics

As explained, the controller 200 may use one of three mathematicaltechniques to determine the predicted data/parameters 272, i.e.,predicted voltage data 272 a and predicted temperature data 272 b. Eachone of the described mathematical techniques may output differentpredicted parameters 272 than the other mathematical techniques. Assuch, the following discussion demonstrates the different performancemetrics of the described mathematical techniques that the controller 200may implement.

The first law of thermodynamics states that energy may be converted fromone form to another with the interaction of heat, work, and internalenergy, but it cannot be created nor destroyed. Mathematically, this isrepresented as:

E=W+Q  (12)

where E is the total change in internal energy of the system, i.e., thebattery system 124, Q is the heat exchanged between the battery system124 and its surroundings, and W is the work done by the battery system124.

Heat capacity C, also known as thermal capacity, is a measurablephysical quantity that is equal to the ratio of the heat added to (orremoved from) an object to the resulting temperature change. Thecontroller 200 may determine the heat capacity for the battery system124 from the following equation:

ΔE=ΔW+ΔQ  (13)

Over a complete charge or discharge cycle ΔE=0, such that:

ΔW=∫ ₀ ^(t) ^(charge) V(t)I(t)dt−∫ _(t) _(charge) ^(t) ^(discharge)V(t)I(t)dt  (14)

The heat capacity C of the battery system 124 at the cycle is given bythe following equation;

$\begin{matrix}{C = {\frac{\Delta \; Q_{i}}{\Delta \; T_{i}} = \frac{\Delta \; W_{i}}{\Delta \; T_{i}}}} & (15)\end{matrix}$

Where ΔT=T_(i) ^(max)−T_(i) ^(min) is a temperature difference betweenthe maximum and minimum temperatures when the temperature is increasingfor the cycle i. FIG. 10 shows an overview of the heat exchange betweenthe battery system 124 and its immediate environment. As shown, thebattery system 124 (for example, a battery string or bank that includesa number of cells/batteries that are connected in series to produce abattery or battery string with the usable voltage/potential) and itssurrounding environment exchange heat. The heat of the battery system124 at cycle i is defined as;

Q=K·(T _(i) ^(mean) ·T _(ambient))^(n) _(|n=1,2)  (16a)

Where

$\begin{matrix}{T_{i}^{mean} = \frac{\left( {T_{i}^{\min} + T_{i}^{\max}} \right)}{2}} & \left( {16b} \right)\end{matrix}$

where K is a factor, T_(mean) is the mean temperature at temperaturerise, and T_(ambient) is the ambient temperature of the externalenvironment of the battery system 124. FIG. 11 illustrates a graph of anexemplary calculation of the maximum and minimum temperature associatedwith each cycle i; while FIG. 12 illustrates a graph of an exemplaryprediction of the heat capacity and heat using thermodynamics equationsand derivations of Equations (12-16b). Thermal Efficiency may be definedas the ratio of the heat utilized to the total heat producedelectrically. The energy efficiency, also called thermal efficiency, isa measure and defined as:

$\begin{matrix}{{EE} = {{1 - \frac{Q_{out}}{Q_{i\; n}}} = {{\left( {1 - \frac{C*\Delta \; T}{Q}} \right)*100\%} = {\left( {1 - \frac{C*\Delta \; T}{K \cdot \left( {T_{i}^{mean} - T_{ambient}} \right)^{n}}} \right)*100\%}}}} & (17)\end{matrix}$

where C, ΔT, T_(i) ^(mean), T_(ambient) are the heat capacity, thedifference between minimum and maximum temperatures at temperature rise,the mean temperature at temperature rise, and the ambient temperature,respectively.

Validation

In some implementations, the controller 200 may validate the predicteddata 272 a, 272 b with data 126 collected from the sensors 123 using theMean Square Error (MSE) equation:

$\begin{matrix}{{M\; S\; E} = {\frac{1}{n}{\sum\limits_{i = 1}^{n}\left( {{\overset{\_}{Y}}_{i} - Y_{i}} \right)^{2}}}} & (18)\end{matrix}$

where Y _(i) and Y_(i) are the predicted and measured data,respectively.

Use Cases

The below two use cases show the accuracy of the algorithms that thecontroller 200 uses to predict the predicted values 272 to maintainsmooth functioning of the energy storage system 120 as well as toimprove its efficiency. However, the algorithms discussed may be used inany use case associated with the energy market.

Use Case 1: Frequency Regulation

Frequency regulation is the injection and withdrawal of power on asecond-by-second basis to maintain a threshold frequency. Morespecifically, an electric power grid transmits power from a power plant110 to the end user using alternating current (AC), which oscillates ata specific frequency (e.g., 60 Hz for the Americas, and 50 Hz for Europeand Asia). A gap between power generation and usages causes the gridfrequency to change. If demand is higher than supply, the frequency willfall, leading to brownouts and blackouts. If the power plants 110generate more power than consumers 130 are using, the frequency goes up,potentially damaging the grid or the electric devices plugged into it.

Due to the recent increase in high variable renewable resources andincreased variability of demand on the customer side, frequencyfluctuations in the power distribution networks 100 have also increased.As such, the network 100 has to continually balance energy supply anddemand in order to maintain a consistent power frequency. Therefore, thecontroller 200 may predict ways to help regulate the frequency of thedistributed power by the constant second-by-second adjustment of powerto maintain the network frequency and thus to ensure network 100stability, while using the functions discussed above. In some examples,the energy storage system 120 aids the power distribution network 100with improving the power quality of the network 100 by implementingfrequency regulation. FIG. 13A illustrates a graph of an exemplarycurrent frequency regulation profile; while FIG. 13B illustrates a graphof an exemplary voltage frequency regulation profile.

High frequency oscillations of power distribution from the power plantare necessary to compensate for deviations in network voltage frequencydue to high oscillations in total network load. In some examples, it isbeneficial to apply a high frequency power signal to adjust anoutput/input of the battery system 124 to compensate for unanticipatedincreases or decreases in a total network power load, allowing nearinstantaneous corrections to power quality issues.

When applying high frequency power, in some examples, the network 10experiences a drop in voltage. This drop in voltage often occurs duringdischarge. For example, when the energy storage system 120 reaches aminimum voltage (0% State of Charge), a power plant 110 is applied tothe battery system 124 to quickly reach full-charge (100% State ofCharge (SOC)) and allow the battery system 124 to function normally.Predicting this 0% SOC state is important to allowing the consumer 130to anticipate the availability of the battery system 124.

In some examples, the controller 200 uses a predefined fixed value tonumerically define the voltage drop. The predefined fixed value may beequal to 350 V. The goal of the suggested algorithm is to predict allthe voltages (i.e., voltage prediction data 272 a) that manifest a valueless than or equal to the fixed threshold (e.g., 350V). The results ofthe algorithm, as well as the measured data, are displayed in FIG. 14. Avisual inspection of FIG. 14 indicates that the predicted results (i.e.,voltage prediction data 272 a) greatly match the measured data.

To quantify the difference between the predicted data 272 and themeasured data, the Root Mean Squared Error (RMSE) may be calculated asdefined in Equation (19):

$\begin{matrix}{{R\; M\; S\; E} = {\left( {\frac{1}{n}{\sum\limits_{i = 1}^{n}\left( {{\overset{\_}{Y}}_{i} - Y_{i}} \right)^{2}}} \right)^{\frac{1}{2}}\mspace{14mu} \%}} & (19)\end{matrix}$

In this case, the RMSE is suggested to be equal to 1.26%, which leads toan accuracy of approximately 98.7%. The accuracy is defined as:

Accuracy=(100−RMSE) %  (20)

The predictive algorithm described above with reference to FIGS. 1-14may be beneficial in many aspects of managing and monitoring the batterysystem 124 when facing this type of use case. For example, thepredictive algorithm provides an accurate, fast, optimized method, basedon accurate feature selections, to improve the accuracy of the predicteddata 272. The predictive algorithm may provide feedback that permits theBMS 122 to adjust the charge and discharge regime of the battery system124 in real time. In other words, the predictive algorithm provides atime of the voltage drop and the magnitude of the voltage relative to apre-defined power request.

In some implementations, the controller 200 uses a scoring methodologybased on a combination of multiple machine learning algorithms topredict the SOC of the battery system 124. For example, the controller200 may use one of a fuzzy logic method, a support vector machine, or adeep neural network (e.g., neural network 300) to accurately predict theSOC of the battery system 124. In this regard, the SOC of the batterysystem 124 at time t may be calculated as defined in Equation (21):

SOC(t)=SOC(t ₀)+γ*∫P(t)_(charge) *Δt dt+∫P(t)_(discharge) *Δt dt  (21)

where SOC(t) is the SOC at time t, P(t)_(charge) is predicted power in acharge mode of the battery system 124, P(t)_(discharge) is predictedpower in a discharge mode of the battery system 124, and γ is thepredicted efficiency.

In some implementations, the controller 200 uses a scale methodology toscale the SOC between zero percent and one hundred percent to allow anoperator to visualize and track the available power capacity of thebattery system 124 and change the BMS system 122.

Use Case 2: Day-Ahead Market

In some implementations, the cost to supply electricity varies duringthe course of a single day. As such, the wholesale price of electricityon the power distribution network 100 reflects the real-time cost forsupplying electricity from the power plant 110. For example, electricitydemand is usually highest in the afternoon and early evening (peakhours), and costs to provide electricity are usually higher at thesetimes. This use case considers that the battery system 124 is chargedduring low-price hours at the day-ahead spot market and then dischargedduring high-price hours. This use case is used to determine theperformance of the energy storage system 120 when discharged atdifferent levels of power for market bidding purposes.

An example of the power profile “Day Ahead Market” use case is providedin FIG. 15A. As shown, the battery system 124 is charged at constantpower (e.g., about time 0-0.25), then discharged with different powers(e.g., about time greater than 2.25) to fulfill the high demand from theenergy market. This operation is repeated for every battery of thebattery system 124.

For purpose of analysis, FIG. 15B illustrates a graph of the measuredand the predicted voltages. As can be noticed, the predictive data 272perfectly fits the measured data. The RMSE is suggested to be equal to0.026% for this example. As such, this leads to an accuracy approaching100%. Considering FIG. 16, illustrating two graphs A, B, the first graphA being a graph of the power/time of the battery system 124 and thesecond graph B being the SOC percentage/time of the battery system 124,it is noticeable that the SOC % decreases due to high power discharge(e.g., about time greater than 2.5). This decrease is most apparent at 4kW, where, the SOC drops to 60%.

Referring to FIG. 17, the prediction algorithms described above may alsopredict a minimum cut-off voltage. This corresponds to the lower voltagelimit, which may be used to initiate a new charge regime allowing thebattery system 124 to function normally, and therefore increase its lifecycle.

Therefore, the prediction algorithms discussed above may provideimportant and beneficial measurements ahead of time. Some of theimportant and beneficial measurements may include the remaining timeduration of the discharge at different powers depending on the marketdemand. Other important and beneficial measurements may include thevoltage, the minimum cut-off voltage, and the SOC needed to monitor thedischarge of the battery system 124, while keeping the battery system124 running smoothly. As such, the distribution network 100 provides theconsumer 130 with a complete array of the status information of thebattery system 124 and system capabilities.

In some examples, the commercially relevant property of a batteryinstallation is calculated from a minimal set of basis functions orbasis variables in the time domain. According to the network 100described above, energy efficiency is the most important property of thebattery installation to be able to predict in the future since itdirectly drives the profitability of the installation and drive biddingstrategies for the energy storage asset. As such, the network 100 isconfigured to determine the forward projected energy efficiency of anenergy storage installation from only the historical time dependentcurrent and time dependent ambient temperature. The methods describedare configured to determine a set of time invariant or slowly timevarying parameters for each energy storage installation and use these toforward predict the performance given an assumed current and temperatureprofile. A biding software application may ask the BMS 122 what theefficiency would be for several different possible future load profilesand then choose the most profitable. The best basis functions to do thiswith appear to be permutations of the set of the current, ambienttemperature, the first and second derivative of current and temperature,and the first and second integral of the temperature and current.

FIG. 18 provides a schematic view of an exemplary arrangement ofoperations for a method 1800 of predicting future battery systemparameters. At operation 1802, the method 1800 includes receiving, atdata processing hardware, current measurements from at least one currentsensor configured to measure current of a battery system incommunication with a power distribution network having a power plantdistributing power to one or more consumers. At operation 1804, themethod 1800 includes receiving, at the data processing hardware, voltagemeasurements from at least one voltage sensor configured to measurevoltage of the battery system. At operation 1806, the method 1800includes receiving, at the data processing hardware, temperaturemeasurements from at least one temperature sensor configured to measuretemperature of the battery system. At operation 1808, the method 1800includes determining, by the data processing hardware, an impedanceparameter of the battery system based on the received measurements. Atoperation 1810, the method 1800 includes determining, by the dataprocessing hardware, a temperature parameter of the battery system basedon the received measurements. At operation 1812, the method 1800includes determining, by the data processing hardware, a predictedvoltage parameter based on the impedance parameter. At operation 1814,the method 1800 includes determining, by the data processing hardware, apredicted temperature parameter based on the temperature parameter. Atoperation 1816, the method 1800 includes commanding, by the dataprocessing hardware, the battery system to charge (e.g., store) powerfrom the power plant or discharge power from the power plant based onthe predicted voltage parameter and the predicted temperature parameter.For example, at operation 1816, the method 1800 may include commanding,by the data processing hardware, the battery system to store power fromthe power plant or discharge power from the power plant based on thepredicted voltage parameter and the predicted temperature parameter.

FIG. 19 is a schematic view of an example computing device 1900 that maybe used to implement the systems and methods described in this document.The computing device 1900 is intended to represent various forms ofdigital computers, such as laptops, desktops, workstations, personaldigital assistants, servers, blade servers, mainframes, and otherappropriate computers. The components shown here, their connections andrelationships, and their functions, are meant to be exemplary only, andare not meant to limit implementations of the inventions describedand/or claimed in this document.

The computing device 1900 includes a processor 1910, memory 1920, astorage device 1930, a high-speed interface/controller 1940 connectingto the memory 1920 and high-speed expansion ports 1950, and a low speedinterface/controller 1960 connecting to low speed bus 1970 and storagedevice 1930. Each of the components 1910, 1920, 1930, 1940, 1950, and1960, are interconnected using various busses, and may be mounted on acommon motherboard or in other manners as appropriate. The processor1910 can process instructions for execution within the computing device1900, including instructions stored in the memory 1920 or on the storagedevice 1930 to display graphical information for a graphical userinterface (GUI) on an external input/output device, such as display 1980coupled to high speed interface 1940. In other implementations, multipleprocessors and/or multiple buses may be used, as appropriate, along withmultiple memories and types of memory. Also, multiple computing devices1900 may be connected, with each device providing portions of thenecessary operations (e.g., as a server bank, a group of blade servers,or a multi-processor system).

The memory 1920 stores information non-transitorily within the computingdevice 1900. The memory 1920 may be a computer-readable medium, avolatile memory unit(s), or non-volatile memory unit(s). Thenon-transitory memory 1920 may be physical devices used to storeprograms (e.g., sequences of instructions) or data (e.g., program stateinformation) on a temporary or permanent basis for use by the computingdevice 1900. Examples of non-volatile memory include, but are notlimited to, flash memory and read-only memory (ROM)/programmableread-only memory (PROM)/erasable programmable read-only memory(EPROM)/electronically erasable programmable read-only memory (EEPROM)(e.g., typically used for firmware, such as boot programs). Examples ofvolatile memory include, but are not limited to, random access memory(RAM), dynamic random access memory (DRAM), static random access memory(SRAM), phase change memory (PCM) as well as disks or tapes.

The storage device 1930 is capable of providing mass storage for thecomputing device 1900. In some implementations, the storage device 1930is a computer-readable medium. In various different implementations, thestorage device 1930 may be a floppy disk device, a hard disk device, anoptical disk device, or a tape device, a flash memory or other similarsolid state memory device, or an array of devices, including devices ina storage area network or other configurations. In additionalimplementations, a computer program product is tangibly embodied in aninformation carrier. The computer program product contains instructionsthat, when executed, perform one or more methods, such as thosedescribed above. The information carrier is a computer- ormachine-readable medium, such as the memory 1920, the storage device1930, or memory on processor 1910.

The high speed controller 1940 manages bandwidth-intensive operationsfor the computing device 1900, while the low speed controller 1960manages lower bandwidth-intensive operations. Such allocation of dutiesis exemplary only. In some implementations, the high-speed controller1940 is coupled to the memory 1920, the display 1980 (e.g., through agraphics processor or accelerator), and to the high-speed expansionports 1950, which may accept various expansion cards (not shown). Insome implementations, the low-speed controller 1960 is coupled to thestorage device 1930 and low-speed expansion port 1970. The low-speedexpansion port 1970, which may include various communication ports(e.g., USB, Bluetooth, Ethernet, wireless Ethernet), may be coupled toone or more input/output devices, such as a keyboard, a pointing device,a scanner, or a networking device such as a switch or router, e.g.,through a network adapter.

The computing device 1900 may be implemented in a number of differentforms, as shown in the figure. For example, it may be implemented as astandard server 1900 a or multiple times in a group of such servers 1900a, as a laptop computer 1900 b, or as part of a rack server system 1900c.

Various implementations of the systems and techniques described hereincan be realized in digital electronic and/or optical circuitry,integrated circuitry, specially designed ASICs (application specificintegrated circuits), computer hardware, firmware, software, and/orcombinations thereof. These various implementations can includeimplementation in one or more computer programs that are executableand/or interpretable on a programmable system including at least oneprogrammable processor, which may be special or general purpose, coupledto receive data and instructions from, and to transmit data andinstructions to, a storage system, at least one input device, and atleast one output device. In some implementations, the computer programs,including the algorithms described herein, are implemented in C++ usingoptimized and fast OPENMP classes and functions.

These computer programs (also known as programs, software, softwareapplications or code) include machine instructions for a programmableprocessor, and can be implemented in a high-level procedural and/orobject-oriented programming language, and/or in assembly/machinelanguage. As used herein, the terms “machine-readable medium” and“computer-readable medium” refer to any computer program product,non-transitory computer readable medium, apparatus and/or device (e.g.,magnetic discs, optical disks, memory, Programmable Logic Devices(PLDs)) used to provide machine instructions and/or data to aprogrammable processor, including a machine-readable medium thatreceives machine instructions as a machine-readable signal. The term“machine-readable signal” refers to any signal used to provide machineinstructions and/or data to a programmable processor.

The processes and logic flows described in this specification can beperformed by one or more programmable processors executing one or morecomputer programs to perform functions by operating on input data andgenerating output. The processes and logic flows can also be performedby special purpose logic circuitry, e.g., an FPGA (field programmablegate array) or an ASIC (application specific integrated circuit).Processors suitable for the execution of a computer program include, byway of example, both general and special purpose microprocessors, andany one or more processors of any kind of digital computer. Generally, aprocessor will receive instructions and data from a read only memory ora random access memory or both. The essential elements of a computer area processor for performing instructions and one or more memory devicesfor storing instructions and data. Generally, a computer will alsoinclude, or be operatively coupled to receive data from or transfer datato, or both, one or more mass storage devices for storing data, e.g.,magnetic, magneto optical disks, or optical disks. However, a computerneed not have such devices. Computer readable media suitable for storingcomputer program instructions and data include all forms of non-volatilememory, media and memory devices, including by way of examplesemiconductor memory devices, e.g., EPROM, EEPROM, and flash memorydevices; magnetic disks, e.g., internal hard disks or removable disks;magneto optical disks; and CD ROM and DVD-ROM disks. The processor andthe memory can be supplemented by, or incorporated in, special purposelogic circuitry.

To provide for interaction with a user, one or more aspects of thedisclosure can be implemented on a computer having a display device,e.g., a CRT (cathode ray tube), LCD (liquid crystal display) monitor, ortouch screen for displaying information to the user and optionally akeyboard and a pointing device, e.g., a mouse or a trackball, by whichthe user can provide input to the computer. Other kinds of devices canbe used to provide interaction with a user as well; for example,feedback provided to the user can be any form of sensory feedback, e.g.,visual feedback, auditory feedback, or tactile feedback; and input fromthe user can be received in any form, including acoustic, speech, ortactile input. In addition, a computer can interact with a user bysending documents to and receiving documents from a device that is usedby the user; for example, by sending web pages to a web browser on auser's client device in response to requests received from the webbrowser.

A number of implementations have been described. Nevertheless, it willbe understood that various modifications may be made without departingfrom the spirit and scope of the disclosure. Accordingly, otherimplementations are within the scope of the following claims.

What is claimed is:
 1. A method comprising: receiving, at dataprocessing hardware, current measurements from at least one currentsensor configured to measure current of a battery system incommunication with a power distribution network having a power plantdistributing power to one or more consumers; receiving, at dataprocessing hardware, voltage measurements from at least one voltagesensor configured to measure voltage of the battery system; receiving,at data processing hardware, temperature measurements from at least onetemperature sensor configured to measure temperature of the batterysystem; determining, by the data processing hardware, an impedanceparameter of the battery system based on the received measurements;determining, by the data processing hardware, a temperature parameter ofthe battery system based on the received measurements; determining, bythe data processing hardware, a predicted voltage parameter based on theimpedance parameter; determining, by the data processing hardware, apredicted temperature parameter based on the temperature parameter; andcommanding, by the data processing hardware, the battery system tocharge power from the power plant or discharge power from the powerplant based on the predicted voltage parameter and the predictedtemperature parameter.
 2. The method of claim 1, wherein determining theimpedance parameter or the temperature parameter comprises determining atransfer function H(w) of a time series f(t) defined in a time interval[−T, T], where T is an integer greater than zero, the transfer functionH(w), in a complex domain, being defined as:H(w)=∫_(−T) ^(+T)∫(t)e ^(−iωt) dt, where w=2πF, F is a frequency of atime series of the received measurements, defined as tεR^(n) andFεC^(n).
 3. The method of claim 2, wherein the transfer function H(w) isdefined as a ratio between a Fourier transform of an output variabley(t) and an input variable x(t), where the output variable y(t) is oneof the impedance parameter or the temperature parameter, and the inputvariable x(t) is one or more of the received measurements, and thetransfer function H(w) in a discrete domain is determined as:${H(w)} = {\frac{\sum\limits_{p = 1}^{N}{{y(p)}e^{{- i}\; \omega \; p}}}{\sum\limits_{p = 1}^{N}{{x(p)}e^{{- i}\; \omega \; p}}}.}$4. The method of claim 1, wherein determining one of the predictedvoltage parameter or the predicted temperature parameter includesexecuting a time series analysis implementing an auto-regressive model.5. The method of claim 4, wherein the auto-regressive model AR(p) isdefines as:X _(t) =c+Σ _(i=1) ^(p)φ_(i) X _(t-i)+ε_(i); where φ₁-φ_(p) areparameters of the model, c is a constant, and ε_(t) is white noise. 6.The method of claim 4, further comprising implementing a neural networkapproach, an empirical recursive method, or a Yule-Walker approach todetermine an optimal solution of the auto-regressive model AR(p).
 7. Themethod of claim 1, wherein commanding, by the data processing hardware,the battery system to charge power from the power plant includescommanding the battery system to store power from the power plant. 8.The method of claim 1, further comprising updating an impedance profile,a voltage profile, or a temperature profile based on the voltagemeasurements or the temperature measurements.
 9. The method of claim 1,wherein determining the predicted voltage parameter includes: trainingthe data processing hardware to generate a best fit of the voltagemeasurements or the temperature measurements; and predicting, by thedata processing hardware, the predicted voltage parameter or thepredicted temperature parameter based on the best fit of the voltagemeasurements or the temperature measurements, respectively.
 10. Themethod of claim 1, further comprising: tracking, by the data processinghardware, a remaining available capacity of the battery system; anddetermining, by the data processing hardware, one of a charge state orlife cycle of the battery system.
 11. A system comprising: dataprocessing hardware; and memory hardware in communication with the dataprocessing hardware, the memory hardware storing instructions that whenexecuted on the data processing hardware cause the data processinghardware to perform operations comprising: receiving currentmeasurements from at least one current sensor configured to measurecurrent of a battery system in communication with a power distributionnetwork having a power plant distributing power to one or moreconsumers; receiving voltage measurements from at least one voltagesensor configured to measure voltage of the battery system; receivingtemperature measurements from at least one temperature sensor configuredto measure temperature of the battery system; determining an impedanceparameter of the battery system based on the received measurements;determining a temperature parameter of the battery system based on thereceived measurements; determining a predicted voltage parameter basedon the impedance parameter; determining a predicted temperatureparameter based on the temperature parameter; and commanding the batterysystem to charge power from the power plant or discharge power from thepower plant based on the predicted voltage parameter and the predictedtemperature parameter.
 12. The system of claim 11, wherein determiningthe impedance parameter or the temperature parameter comprisesdetermining a transfer function H(w) of a time series f(t) defined in atime interval [−T, T], where T is an integer greater than zero, thetransfer function H(w), in a complex domain, being defined as:H(w)=∫_(−T) ^(+T) f(t)e ^(−ωt) dt, where w=2πF, F is a frequency of atime series of the received measurements, defined as tεR^(n) andFεC^(n).
 13. The system of claim 12, wherein the transfer function H(w)is defined as a ratio between a Fourier transform of an output variabley(t) and an input variable x(t), where the output variable y(t) is oneof the impedance parameter or the temperature parameter, and the inputvariable x(t) is one or more of the received measurements, and thetransfer function H(w) in a discrete domain is determined as:${H(w)} = {\frac{\sum\limits_{p = 1}^{N}{{y(p)}e^{{- i}\; \omega \; p}}}{\sum\limits_{p = 1}^{N}{{x(p)}e^{{- i}\; \omega \; p}}}.}$14. The system of claim 11, wherein determining one of the predictedvoltage parameter or the predicted temperature parameter includesexecuting a time series analysis implementing an auto-regressive model.15. The system of claim 14, wherein the auto-regressive model AR(p) isdefines as:X _(t) =c+Σ _(i=1) ^(p)φ_(i) X _(t-i)+ε_(i); where φ₁-φ_(p) areparameters of the model, c is a constant, and ε_(t) is white noise. 16.The system of claim 14, wherein the instructions, when executed on thedata processing hardware, cause the data processing hardware to performoperations comprising: implementing a neural network approach, anempirical recursive method, or a Yule-Walker approach to determine anoptimal solution of the auto-regressive model AR(p).
 17. The system ofclaim 11, wherein commanding, by the data processing hardware, thebattery system to charge power from the power plant includes commandingthe battery system to store power from the power plant.
 18. The systemof claim 11, wherein the instructions, when executed on the dataprocessing hardware, cause the data processing hardware to performoperations comprising: updating an impedance profile, a voltage profile,or a temperature profile based on the voltage measurements or thetemperature measurements.
 19. The system of claim 11, whereindetermining the predicted voltage parameter includes: training the dataprocessing hardware to generate a best fit of the voltage measurementsor the temperature measurements; and predicting, by the data processinghardware, the predicted voltage parameter or the predicted temperatureparameter based on the best fit of the voltage measurements or thetemperature measurements, respectively.
 20. The system of claim 11,wherein the instructions, when executed on the data processing hardware,cause the data processing hardware to perform operations comprising:tracking a remaining available capacity of the battery system; anddetermining one of a charge state or life cycle of the battery system.